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Résumé |
Symmetries are one of the major tools to understand the
structure of physical theories. However, even the most powerful symmetry
is useless if it is hidden and, therefore, not accessible in
calculations. Prominent examples are S-, T-, and U-dualities of
superstrings and branes. They unify the five perturbative superstring
theories and M-theory into a single framework. Still, their imprints on
the low-energy effective supergravity theories are subtle and easy to
miss. A framework that addresses this issue is (exceptional) generalized
geometry. Although thought of as a natural extension of geometry to an
extended tangent bundle, it still lacks fundamental objects of
differential geometry like the Riemann tensor. After a short review of
the most important differences between generalized and standard
differential geometry, I will present the underlying cause for this
trouble and present a proposal for a solution that gives a new,
geometric perspective on duality symmetries in supergravity. This
approach will not just resolve some old puzzles but it also has direct
applications, leading to a much broader notion of dualities in
supergravity that can be used to generate new solutions and even
higher-derivative corrections. |
